Locally logical mathematics: An emerging teacher honoring both students and mathematics |
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| Institution: | 1. The Pennsylvania State University, 270 Chambers Building, University Park, PA 16802, USA;2. University of Louisville, Porter Education Building, Louisville, KY 40292, USA;3. West Chester University of Pennsylvania, 700 South High Street, West Chester, PA 19383, USA;4. Bald Eagle School District, 751 S. Eagle Valley Road, Wingate, PA 16823, USA;5. Northern Kentucky University, Nunn Drive, Highland Heights, KY 41099, USA;1. University of Alicante, Spain;2. University of Leuven, Belgium;1. Resuscitation for Medical Disciplines Research Group, The Medical School, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom;2. Heart of England NHS Foundation Trust, Bordesley Green East, Birmingham B9 5SS, United Kingdom;3. Queen Elizabeth Hospital Birmingham, University Hospitals Birmingham NHS Foundation Trust, Birmingham B15 2WB, United Kingdom;4. Sandwell and West Birmingham Hospitals NHS Trust, Birmingham City Hospital, Dudley Road, Birmingham B18 7QH, United Kingdom;1. Department of Mathematics and Science Education, University of Georgia, 105G Aderhold Hall, Athens, GA 30602-7124, United States;2. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States;1. University of Warwick, UK;2. Bandeirante University of São Paulo, Brazil;1. Tel-Aviv University, Israel;2. The Weizmann Institute, Israel;3. San Diego State University, United States |
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| Abstract: | This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks. |
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| Keywords: | Teaching practice Mathematical processes Prospective secondary mathematics teacher Teacher knowledge |
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